Incremental harmonic balance method for nonlinear flutter of an airfoil with uncertain-but-bounded parameters

Chen, Y.M.; Liu, J.K.; Meng, Guang

doi:10.1016/j.apm.2011.07.016

Cited by 35 publications

(29 citation statements)

References 30 publications

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“…Numerical simulations in nonlinear aeroelastics can be performed based on the state space models [6,7]. These models were generally solved by time-marching integration techniques such as the Runge-Kutta (RK) and Newmark methods, etc [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Simulating nonlinear aeroelastic responses of an airfoil with freeplay based on precise integration method

Cui

Liu

Chen

2015

Communications in Nonlinear Science and Numerical Simulation

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Section: Introductionmentioning

confidence: 99%

Simulating nonlinear aeroelastic responses of an airfoil with freeplay based on precise integration method

Cui

Liu

Chen

2015

Communications in Nonlinear Science and Numerical Simulation

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“…Yoon and Yoon [9] employed the HBM to investigate the dynamic characteristics of a single-degree-of-freedom (DOF) torsional system accompanied by a multi-stage clutch damper model. Other studies have examined various vibration problems using the HBM [10][11][12][13][14][15][16][17][18][19][20][21][22]. For instance, nonlinear problems using a Duffing oscillator or cubic stiffness have been settled by utilizing the nonlinear output frequency response functions (NOFRFs) and incremental harmonic balance (IHB) method [10,11].…”

Section: Introductionmentioning

confidence: 99%

Vibro-Impact Energy Analysis of a Geared System with Piecewise-Type Nonlinearities Using Various Parameter Values

Yoon

Kim

2015

Energies

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Torsional systems with gear pairs such as the gearbox of wind turbines or vehicle driveline systems inherently show impact phenomena due to clearance-type nonlinearities when the system experiences sinusoidal excitation. This research investigates the vibro-impact energy of unloaded gears in geared systems using the harmonic balance method (HBM) in both the frequency and time domains. To achieve accurate simulations, nonlinear models with piecewise and clearance-type nonlinearities and drag torques are defined and implemented in the HBM. Next, the nonlinear frequency responses are examined by focusing on the resonance areas where the impact phenomena occur, along with variations in key parameters such as clutch stiffness, drag torque, and inertias of the flywheel and the unloaded gear. Finally, the effects of the parameters on the vibro-impacts at a specific excitation frequency are explained using bifurcation diagrams. The results are correlated with prior research by defining the gear rattle criteria with key parameters. This article suggests a method to simulate the impact phenomena in torsional systems using the HBM and successfully assesses vibro-impact energy using bifurcation diagrams.

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“…This phenomenon is associated with the NVH performance (vibration and noise) of the target system and is highly nonlinear behavior, and difficult to analyze. In order to investigate nonlinear dynamic responses in a simple mechanical system, many studies have been conducted using the harmonic balance method (HBM) [4][5][6][7][8][9][10][11][12]. For example, Peng et al [4] suggested nonlinear output frequency response functions using the Duffing oscillator to simulate strong nonlinear equations.…”

Section: Introductionmentioning

confidence: 99%

“…Al-shyyab and Kahraman [5] investigated sub-harmonics and chaotic motions in a multi-mesh gear train using a nonlinear time-varying dynamic model. Chen et al [6] used the incremental harmonic balance (IHB) method to investigate the limit cycle oscillation of a two-dimensional airfoil with parameter variability in an incompressible flow. Genesio and Tesi [7] presented two practical methods to predict the existence and the location of chaotic motions.…”

Section: Introductionmentioning

confidence: 99%

Effect of Various Excitation Conditions on Vibrational Energy in a Multi-Degree-of-Freedom Torsional System with Piecewise-Type Nonlinearities

Yoon

Kim

2015

Energies

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Dynamic behaviors in practical driveline systems for wind turbines or vehicles are inherently affected by multiple nonlinearities such as piecewise-type torsional springs. However, various excitation conditions with different levels of magnitudes also show strong relationships to the dynamic behaviors when system responses are examined in both frequency and time domains. This study investigated the nonlinear responses of torsional systems under various excitations by using the harmonic balance method and numerical analysis. In order to understand the effect of piecewise-type nonlinearities on vibrational energy with different excitations, the nonlinear responses were investigated with various comparisons. First, two different jumping phenomena with frequency up-and down-sweeping conditions were determined under severe excitation levels. Second, practical system analysis using the phase plane and Poincaré map was conducted in various ways. When the system responses were composed of quasi-periodic components, Poincaré map analysis clearly revealed the nonlinear dynamic characteristics and thus it is suggested to investigate complicated nonlinear dynamic responses in practical driveline systems.

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Incremental harmonic balance method for nonlinear flutter of an airfoil with uncertain-but-bounded parameters

Cited by 35 publications

References 30 publications

Simulating nonlinear aeroelastic responses of an airfoil with freeplay based on precise integration method

Simulating nonlinear aeroelastic responses of an airfoil with freeplay based on precise integration method

Vibro-Impact Energy Analysis of a Geared System with Piecewise-Type Nonlinearities Using Various Parameter Values

Effect of Various Excitation Conditions on Vibrational Energy in a Multi-Degree-of-Freedom Torsional System with Piecewise-Type Nonlinearities

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